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Re: Circle-circle tangent puzzle
Posted:
Jun 15, 2012 11:53 AM
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> Let A, B be the centers of two circles with radius
> r1, r2 respectively, where r1-r2 is very small.
> Construct the exterior tangent to the given circles.
>
> In this puzzle is sought a practical construction on an A4 sheet of paper that avoids entirely the use of r1-r2.
Let AA0 be the radius of (A,r1) perpendicular to line AB
Let BB0 be the radius of (B,r2) perpendicular to line AB
From A drop perp AA1 to line A0B0
From B drop perp BB1 to line A0B0
Produce AA1 to meet circle(A,r1) in A12
Produce BB1 to meet circle(B,r2) in B12
Line A12B12 is a close approx to the required tangent.
A second iteration, by dropping perps from A and B to line A12B12 and extending these to A22B22 will be only marginally more accurate for the tangent line, but it will give a slight improvement of the location of the points of tangency.
Regards, Peter Scales.
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